This course is an introduction to the notion of risk, its relation to return, and the valuation of projects and companies. This is a capstone course to help you value projects and companies by applying your understanding of time value of money (TVM) and cash flows developed in the first three courses of this specialization. This course is part of a specialization titled “Foundational Finance for Strategic Decision Making” and is helpful if you are interested in applying to an MBA degree program or learning the foundations of finance to be more effective in your career.
The pedagogy of the course is applied and problem-based with assignments covering every part of the course that each contain multiple problems that, by design, are introductory and simpler than the more real-world applications you will confront in the real world and more advanced courses. The assignments are all designed by the faculty lead and machine graded.

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Calculating the return of a project, Calculating the risk of a project, Valuing Projects, Valuing Companies

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Week 2: Diversification, Risk & Return

During this second week of the course, we will introduce one of the most powerful and intuitive model of modern finance - the Capital Asset Pricing Model (CAPM) - that forms the basis of our understanding of the relation between risk and return.

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Gautam Kaul

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Hi. Welcome back. I know today has been depending on what today means to you. You have been taking breaks hopefully. This week has been little bit of a tangent, but I want a topic that's requires you to go and unattended. I remind you again that we just did statistics and we have done that part of statistics that's completely necessary for us to move forward. However, I guarantee you that if you do this statistics and if only practice with the assignments I've given you, then what will happen is, the same skill set will translate into other discipline. So, if you remember what we did in each, with the distribution, with means, with variances, with co-variances, with regression. We basically said that we could use any data or any example, and I purposely, following my general practice, I just pull out examples while I'm talking that, those that could relate to you. And that's the beauty of statistics. As I said, I almost think sometimes like, statistics has got an edge over finance. Almost. Okay. So let's get back to, why did we do statistics? The beginning was about risk and return. And we know why were are doing risk and return. Because we want to figure out the cost of capital. But, as always, I am not going to, in spite of the fact that we are, have statistics now in a little tool kit. We are not going to use formulas. I'm going to go back to why are we doing this? Why risk and return? So. We all know that we are risk averse, and experiments have been conducted to show that that's the case. But we like return. And turns out that if you look at data which I will in a second, and that will be the, some really cool data today will be wrap up of this week, to give you a sense of how reality and the concepts match up so well together. But we like return, and most of us are prepared to take on some risk. So, if we were so risk-averse that we didn't take on any risk, I think it would be a kind of sad situation but then things would be very different. Now we are thinking about taking on risk. However, we don't like it. The good news is we like the return piece of it. But how do we take the risk, given that we our risk covers. We are taking the risk with what in mind, you will see in some kind benefit or return in mind otherwise we wouldn't do so and that's the punch line. But how do we take risk, given that we are risk averse? We hold large, diversified portfolios. And I emphasize again before I even talk about this, that a lot of this part requires individual investment in a thought process that lets do you so. And there are a lot of people in the world who can barely consume enough to survive for the next day. So, I always feel like we have to keep that in mind. That till the world is such a place where all of us can think like this at our individual levels. And not have you know, stocks and bonds in every portfolio but think about the fact that you can save for the future would be a wonderful world to be in. It's not. However, there is a lot of activity in markets, and the hope is more and more families can take advantage of the market place and hope but four years that a large and diversified. So, why am I saying large and diversified? Why don't I just say large? And you will see in a second, and we will do this next week. Is that large alone, doesn't mean anything. Imagine if you are really fascinated by technology, but you're risk-averse, you could hold a very large technology portfolio. In fact Fidelity and other Vanguard and other companies, create such portfolios within industry still. You could hold a very large technology portfolio but it wouldn't be diversified. It may be diversified within technology, but it's not diversified across all aspects of life. So in some sense the diversification is more important than large and we'll see, we'll see explicitly next week why that's the case. Now, why are we talking about this? Because the process of holding a diversified portfolio is an attempt to deal with your queasiness in your stomach when you see risk. But what that leads to is the following phenomena. The queasiness is will make you hold large portfolios and take risk only if there is some kind of a positive relationship between return and risk. So here, here's is another reason why I like this and anything that I have talked about in finance. Is that, its not shockingly counter intuitive. It took a lot of effort to boil down a lot of thinking and work to simple things. But it's the simplicity of the eventual outcome. That's the awesomeness of finance. That's why I like it. It, it's extremely intuitive. So everybody would agree that if we are risk-averse, we like return, we'll take risk only through putting, spreading our wealth or whatever across multiple assets and diversify our portfolio. But even then we'll do that only if we benefit from it, right? Otherwise, what's the point taking risk? So, I hope everybody kinda gets this. I'm going to spend now two significant chunks of time on something that will be on the slide, on available for you to look at, and I'll go back and forth talking about these numbers. The good news is, all these numbers are real. The bad news is there are some numbers, there are tons of numbers as we go along, so just bear with me. Okay. Does US data for example reenforce the intuition. That is, the intuition being that, is there a relationship between taking on risk and the return we get? So this data is very famous data. Almost every textbook reports American data, and there is a bias toward American data, simply because, in about, in about 1926, I know the University of Chicago started collecting, going back and collecting data which is very clean data, and then with the development of technology, more data has been available. But this is clean data, very well measured and so on, and not just randomly selected data. And this data I will talk about, does not preclude you from looking at data in different countries, but I guarantee you the pattern that we'll see here will emerge in any country, any context that you're thinking of. One more thought, all the data I'm showing you has to do with things that trade easily, so stocks and bonds. I want to caution you that, that is not the entire investment of even the American people or outside people in America. Why? Because there are other assets out there. One of which is what? You. Human capital. The belief is as a country progresses economically. More and more of it's investments happen in the human capital development. Education and service industries kind of develop faster as you go. So there is controversy about that, that, should you, should America be only a service industry based country and somebody else should do all manufacturing. And I would recommend to you sometimes reading economists because they have some very cool back and forth by leading experts on issues like that. I just wanted to caution you about the fact that this does not measure everything. However, the fact is it measures a ton and for a bunch of beers. Another point to write up if you see the slide up there, it's 1926 to 2008, U.S. Experience, and everything I'm showing you is portfolios. Why am I showing you portfolios? Because although later in the next slide, I will show you individual securities, I want you to recognize that when you say risk aversion, you almost automatically have to talk about portfolios. Otherwise what happens is, if you say risk aversion and talk only individual securities, there's a mismatch. Your behavior has to match your instincts and your instincts, all of us are, is to spread our wealth around if we have some. Right? Okay, so let's get started. The first column, and stare at it, is different types of assets. So the first asset is a portfolio of small stocks. And it's not, stocks that are small but, company that are small. The reason they are separated out is initially small stocks are more risky. Research shows they are early in their stage of development. So there's this separate kind of category made here. S and P 500 is Standard and Poor's 500 stocks, and they are collected in such a fashion, that the hope is that they measure all sectors of the economy. So as you see later, an important, it'll play an important role in how we measure risk. The next category is corporate bonds. Remember, we talked about corporate bonds largely being a U.S. Phenomena. But corporate bonds are the next category within say, the riskiness dimension. Next to it is, I mean after it is government bonds. What are government bonds? These are bonds that are coupon paying and typically long term and finally T bills, which are treasury bills are the most traded asset probably in the entire world. These are up to one year maturity, zero coupon bonds. Now turns out there are zero coupon bonds that of longer maturity but they are called strips. And I will talk about that it's not that important to this discussion but strips are simply more than one year maturity zero coupon bonds. What is on the next column heading? Average returns, and you know how to calculate that. That's why I did some data statistics with you. So, what is 21%. 21 percent is the annual return on a large set of small stocks. So there is averaging going on twice. One is over time, the second is across of lot of stocks. So this number is, doesn't have too much error in terms of saying it's just one stock. It's a large portfolio. So hopefully, this measures something that has happened in the past pretty accurately. That's what would you get. Average rate of return, and what is return? Let's just go back to our fundamentals, our return has two components almost always. In the case of bonds, it's coupon and when you settle a bond, what do you get? In the case of a stock, it, the coupon part is called a dividend. It's not a, it's not promised or anything. That's the, in fact, the beauty of stocks. And the second component is capital gain or loss during the year, change in prices. Okay, so you calculate the return, it's 21%. Look what the next number is. Twelve%, the difference is nine%. That's a huge difference. I would encourage you at the end of this to take $100 and make investments in 1926. Remember we did this. And see the future value today of these investments. So suppose you put hundred dollars in small stocks, hundred in S and P 500, hundred in corporate, you will see what will happen. There'll be a dramatic drop as you go down, or increase as you go up. Okay? S and P 500 twelve%, corporate bonds seven%, government bonds six percent and T-bills four%. Now let's pause there for a second and ask the following question. Suppose you didn't know much about finance but you knew what a return was. And you had some sense of you know, what riskiness is. Doesn't a pattern emerge? I think a pattern already emerges that risky things than to give a much higher return. So in the next column is the average risk premium. And let me define what that means. That is the difference between the portfolio that's risky and something that's not risky. And we know that if you believe the government is going to pay up, the not risky thing is the treasury bill. So the 21 percent goes to a seventeen percent becomes a seventeen percent average risk premium because I've just subtracted four percent from it. So as we go along, I'm going to just start, first I want to show you all the numbers. And then I'm going to start you know, drawing a little bit on this. Not much, yes, a little bit. So what's the average risk premium on the S and P 500? Eight%. Three percent on corporate bonds, and two percent on government bonds. The reason for corporate and government bond difference is pretty obvious, right? It's something that you believe could default versus something that can't, or wouldn't, most probably. So, till now, we are okay. So there is a dropping pattern of returns which is significant, right. The seventeen percent difference and that small. In fact, this is [unknown]. In fact, I would say the eight percent difference on the S and P 500 kind of captures the market more, of more in a representative way than small stocks, because large stocks dominate the marketplace, because they're big in, in size, as in market cap and so on. Okay. So let's now look at the last column, and this is the punchline. Look at the standard deviation. Remember we calculated it, its the variances square root. So the mean is 21%, the standard deviation of small stalks is twice the size of the [laugh] mean. So this tells you that return comes with risk, and may be a lot of risks even though its a portfolio. And that's life, you know? But lets go to S and P 500. What happens? The return drops substantially to twelve%, and standard deviation is half of that of small stocks. Go down one more. Return drop some more. What happens to standard deviation for government bonds? Drops drastically. Go, go to government bonds. And this is the only slight anomaly where the standard deviation is slightly off. But this is data, and remember the standard deviation estimates are measured with a lot of error. And finally, treasury bills. So the reason standard deviation is there in treasury bills is we are looking at a rate of return, right? Now, you stare at all these numbers, one pattern jumps at you, which is the following. Our gut tells us that if we are risk-averse, we will only take on risk if there is commensurate return in response. Turns out, the data supports that. And I would say pretty strongly on a broad level. I'm not going to write a paper based on this. And even if I could, you know. [laugh] even I would laugh at the paper, because this is very simplistic data analysis. But it's pretty powerful too. That on a average, large portfolios support the notion that we are risk averse. So I'm, I'm trained in always using data to test my thinking. And I think that's an awesome thing that happen, happened with me. I mean, that's how I did my research, and I think like that. I think that's the kind of thinking that you need to carry with you. Is that, if you make a statement, you better be willing to support it with data. It's not a personal statement, right? Otherwise life would be miserable. If you were to adore someone, you know I love you and you show me the data. I mean that's going to be little miserable way of living. But, you know what I mean. So this is one set of data and I want move on to the next one. But before I do, I promised you I would just Draw one line. And I also, as I am looking at it, I want to make sure you get what I am saying. Return goes up. What happens at the same time? Risk goes up. So return and risk are joined at the hip. You know what I mean? They're literally joined at the hip. Now, let me ask you one question before we go on. Suppose you observe that somebody is holding a portfolio with low risk versus somebody else is holding a portfolio with high risk. Does that mean anything about judgment? What can you say about that? Remember one thing about return and risk which the real world always forgets and you will too and I too, do too. We start focusing on one of it. All the newspapers only talk about this. They never talk about this. Almost never. And that, to me, is a tragedy. For example, open up a newspaper, even the best newspapers of the world will say, portfolio X has done better than the S and P 500 nine out of the last ten years. That doesn't mean anything to me. I mean it's, it to me, that's useless information. Why? Unless you say that the risk of S and P 500 was higher than this portfolio in every year, you are not telling me anything. Why? Because whenever you see a return, it comes with risk. And here again, markets are very important. In a market that has gone on for so long, for 80 years, 82 years. The hopefully, over time, it has become more efficient and reflecting risk and return opportunities as matching each other. Talking about the last 80 years, one final talk. If you look at the risk premium on the S and P 500 of nine%, what do you notice is that's it's a very, very large number. I hope you notice that. This number is, has been around seven percent in most data when you compare it to other large portfolios and so on and that's the turn we carry in our head. Turns out, if you look historically at all stock markets of the world, and they have existed and gone and disappeared, data shows this number is much lower, and that the American experience of the last 80 to 90 years is an aberration. To give an example, it has a survival bias in it. I think, though there's no proof of this, there is enough data pointing to that and intuition suggests that too, that we are not suddenly more risk averse in the US, people are people all over the world, right? So, what, what could be the reason for this huge rate of return and difference compared to other stock markets, or even the US before 1926. Their could be several reason. Am, as many as you can think of but I want to point out itself, why we will has one of the reason is because, it's very tough to come up with other explanations that make as much sense. So just keep that in the back of your mind. Why is it important? Because we're going to use this risk premium and all these numbers to, think of our, future. We have to be really careful when using the past to predict the future. Okay? So let's go on to one last thing and then we'll take a break today. I'm going slow in this part because this data is very intuitive and useful and it's not hopefully too painful for you. Okay? I'm going to start and show you this and start with this next time. What is this? This is a portfolio, set of portfolios. Sorry, this is one portfolio right at the S and P 500 for '89 to 2008 period, different from the period we saw before. And in this I am showing you largely what? I am showing you stocks. Disney, AT&T, Pfizer, General Motors, Alcoa, Home Depot, General Electric, Exon, Intel, Citibank, Proctor and Gamble. So I've just picked some stocks and then approximate standard deviation, right? Because I'm not putting decimals and so on, so I'm not going nuts. I want you to just think of one thing. And we'll raise issues today and pickup next time. Next time this will be most of our recap, context. Okay? So stay out of these numbers. Think about the one thing that jumps out at you. But stare at it. Think about the one thing that jumps out at you. Write it down. And this is over and above all your assessments and homeworks, which are largely what? Statistics this week, with financial applications, right? So the homework is not that intense, by the way. But you're doin statistics so that it gets familiar, so please do that. So please do that. But this is your next homework. Tell me what is the one thing that stares out at you? And once you've identified that one thing, please write it down. And then think about the second point. Why does that one thing happen? What is going on? What is, why, why, how do you come up with an explanation of that one thing? Okay? And so the next slide ends with what the heck is going on. So at this point, I am going to leave you with this data, and I'm going to leave it up there. What I will also do is I will put this data in the little, both data pieces, in the little note for you to look at. So like your assignments are on the web, this will we on the web. And I want you to think very carefully about the one thing, don't give me three, the one thing that stands out about this data. And then try to write down what the heck is going on. I don't think that's asking for too much. See you next week, and it's going to be fascinating because we are looking at data, and then trying to make sense of it. Bye now.